[en] The exact solution of the problem of electron phase transitions in the simplest model of electronic structure of rare-earth compounds is obtained taking into account the interaction of S and f electrons within the strong coupling limit. Thermodynamic characteristics (energy, heat capacity, equation of state) are calculated and valency behaviour under pressure is analyzed. It is shown that in the absence of the interaction with the lattice the phase transitions turn out smooth everywhere (of the II order). The allowance for the interaction of the electrons with the lattice homogeneous deformation results in the possibility of jumplike phase transitions. The comparison with other approximate solutions of the problem is presented and it is shown that only the generalized self-consistent method gives results close to the exact ones. These results are in agreement with those obtained in the Anderson lattice model and in good qualitative agreement with the evailable experimental data for rare-earth compounds like SmS, SmTe etc